2. 外语
  3. Solve the problem and indicate the best of the answer choices given. NUMBERS: All numbers used are real numbers. FIGURES:

Solve the problem and indicate the best of the answer choices given. NUMBERS: All numbers used are real numbers. FIGURES:

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问题    Solve the problem and indicate the best of the answer choices given.
   NUMBERS: All numbers used are real numbers.
   FIGURES: A figure accompanying a problem-solving question is intended to provide information useful in solving the problem. Figures are drawn as accurately as possible EXCEPT when it is stated in a specific problem that its figure is not drawn to scale. Straight lines may sometimes appear jagged. All figures lie in a plane unless otherwise indicated.
The following data sufficiency problems consist of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of counterclockwise), you must indicate whether
   Ａ. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
   Ｂ. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
   Ｃ. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
   Ｄ. EACH statement ALONE is sufficient.
   Ｅ. Statements (1) and (2) TOGETHER are NOT sufficient.
If p is a positive integer, and p≠0, is an integer?
   (1) p is an even number
   (2) p is a multiple of 3
选项
答案A
解析 One way to verify this is to plug in even numbers; the results soon show that the result is always half of p plus 1/2, which is never an integer. You could also simplify the equation to , and since an even number plus 1 is always an odd number, dividing the sum by 2 will never produce an integer. So statement (1) alone is sufficient. Statement (2) results in integers if p is an odd multiple of 3, but in non-integers if p is an even multiple of 3, so this statement alone is not sufficient.
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